1. Field of the Invention
The present invention relates in general to systems for measuring the noise figure of a radio frequency device and in particular to a system for measuring noise figure employing a randomly modulated signal as a device stimulus.
2. Description of Related Art
Noise figure F, a commonly used measure of the noise produced by radio frequency devices, is defined as the signal-to-noise ratio P.sub.SI /P.sub.NI of the device's input signal divided by the signal-to-noise ratio P.sub.SO /P.sub.NO of the device's output signal: EQU F=(P.sub.SI /P.sub.NI)/(P.sub.S0 /P.sub.N0) [1]
An electronic device has a gain (or loss) G where EQU G=P.sub.SO /P.sub.SI [2]
The output signal noise P.sub.NO of any device includes a component GP.sub.NI, the amplified noise in the device's input signal, and an "added noise" component P.sub.NA generated by the device itself: EQU P.sub.NO =GP.sub.NI +P.sub.NA [3]
From equations [1]-[3] we have: EQU F=1+P.sub.NA /GP.sub.NI [4]
From equation [4] we see that the value of the noise figure F for a device depends on the amount of noise P.sub.NI in its input signal. In order for noise figure F to be a meaningful measure of noise a device produces, we must standardize the magnitude of the input signal noise P.sub.NI used when testing devices for noise figure F. It is also important to use an input signal having a relatively small noise power P.sub.NI, since for high values of P.sub.NI the quantity GP.sub.NI in equation [4] could overwhelm the added noise P.sub.NA, thereby consigning noise figure F to a narrow range of values near 1, particularly for high gain devices. By using a small standard input noise power we not only standardize the meaning of F but we also provide a wide range of possible values of noise figure F with which to characterize the noisiness of radio frequency devices.
The standard input signal noise power P.sub.NI used when measuring noise figure F is the very small noise power P.sub.0 produced by a resistor operating at a room temperature, specifically 290 degrees Kelvin. A resistor of any size will generate the same amount of noise power. A resistor's noise power P.sub.N is evenly distributed over the radio frequency range and has a value in any frequency band of width B that is proportional to resistor temperature T, EQU P.sub.N =kTB [5]
where k is Boltzmann's constant. A resistor held T.sub.0 =290 degrees Kelvin will accordingly generate a standard noise power P.sub.0 over any narrow bandwidth B where EQU P.sub.0 32 kT.sub.0 B [6]
Since P.sub.0 has a relatively small value of 4.004.times.10.sup.-21 Watts for each Hertz of bandwidth B, the radio frequency noise generated by a resistor at 290 degrees Kelvin makes a suitable power standard for noise figure testing.
Suppose we connect a resistor held at T.sub.0 =290 degrees Kelvin between ground and the input of a radio frequency device, for example an amplifier of gain G, to be tested for noise figure F. If the resistor is matched to the impedance of the amplifier input, Z.sub.in =Resistance, then the input signal is only noise from the resistor, its output signal will be a combination of an amplified version GP.sub.0 of the input signal P.sub.0 and the amplifier's own added noise P.sub.NA. By substituting P.sub.0 for P.sub.NI in equations [3] and [4] we have EQU P.sub.NO =GP.sub.0 +P.sub.NA [7] EQU F=1+P.sub.NA /GP.sub.0 [8]
Substituting equation [7] into equation [8] we have, EQU F=1+(P.sub.NO -GP.sub.0)/GP.sub.O [9]
Since the input signal noise power P.sub.0 =KT.sub.0 B is known over any narrow frequency band of interest B, then by measuring the amplifier's output power P.sub.NO over that band of interest we can calculate noise figure F from equation [9].
While the standard precisely defines F, it is not always practical to test a device under test (DUT) for noise figure F by applying the signal produced by a resistor held at 290 degrees K as a test signal input to a DUT. Since the value of F depends on the difference between P.sub.NO and GP.sub.0, then when the gain G of the DUT is too large or too small, a test signal input of P.sub.0 may produce an output signal power P.sub.NO that is too large or too small to be accurately measured. The well-known "Y-factor" method determines noise figure F in a manner that satisfies the standard definition of noise figure and yet allows us to employ test signal powers that may be larger or smaller than P.sub.0.
In the Y-factor method we measure the power output P.sub.HO of a radio frequency DUT when it is stimulated by the noise produced by an equivalent resistor at a some "hot" temperature T.sub.H and again measure the DUT output power P.sub.CO when the amplifier is stimulated by a resistor at some "cold" temperature T.sub.C. We then compute noise figure F from the measured values of P.sub.HO, P.sub.CO, T.sub.H and T.sub.C.
FIG. 1 represents a radio frequency DUT 10 as an ideal (noiseless) amplifier 12 having a gain (or loss) G and a noise generator 14 producing "excess" noise power P.sub.E. The excess noise power is represented as being equivalent to the noise power output of a resistor at some temperature T.sub.E : EQU P.sub.E =kT.sub.E B [10]
The output of noise generator 14 drives the input of a summer 16. When an external resistor 18 held at a temperature T.sub.I drives another input of summer 16, summer 16 adds the resistor's output power P.sub.I =kT.sub.I B to the DUT's excess noise power P.sub.E and supplies the result to ideal amplifier 12. Amplifier 12 then amplifies its input signal with gain G to produce an output signal of power EQU P.sub.NO =GkB(T.sub.I +T.sub.E) [11]
The quantity GkBT.sub.E is simply another way of expressing the added noise P.sub.NA produced by device 10.
The well-known "Y-factor" for a device driven alternatively by noise signals from resistors at hot and cold temperatures T.sub.H and T.sub.C is defined as EQU Y=P.sub.HO /P.sub.CO [12]
where P.sub.HO is the power of the device output signal produced in response to the hot temperature resistor and P.sub.CO is the power of the device output signal produced in response to the cold temperature resistor over some frequency band of interest. If we substitute P.sub.HO for P.sub.NO and T.sub.H for T.sub.I in equation [11] we have EQU P.sub.HO =GkB(T.sub.H +T.sub.E) [13]
If we substitute P.sub.CO for P.sub.NO and T.sub.C for T.sub.I in equation [11] we have EQU P.sub.CO =GkB(T.sub.C +T.sub.E) [14]
Substituting equations [13] and [14] into equation [12] and solving for T.sub.E we have EQU T.sub.E =(T.sub.H -YT.sub.C)/(Y-1) [15]
Since P.sub.NA =GKBT.sub.E, then from equation [8] EQU F=1+P.sub.E /P.sub.0 [16]
Since P.sub.E =KT.sub.E B and P.sub.0 =KT.sub.0 B then from equation [16] EQU F=1+T.sub.E /T.sub.0 [17]
Substituting equation [15] into equation [17] and rearranging terms, we have EQU F=[(T.sub.H /T.sub.0- 1)-Y(T.sub.C /T.sub.0- 1)](Y-1) [18]
Thus with resistor temperatures T.sub.H and T.sub.C known, and with T.sub.0 a known constant, then we can measure P.sub.HO and P.sub.CO, compute Y in accordance with equation [12] and then compute F using equation [18]. Note that equation [18] is independent of bandwidth B. As long as the DUT output powers P.sub.HO and P.sub.CO are measured over the same bandwidth, it is not necessary to know the exact bandwidth over which the measurements are taken.
While this prior art Y-factor method of measuring noise figure F solves some problems, it requires the use of two resistors held at two different temperatures T.sub.H and T.sub.C or electrically equivalent noise power that must be accurately known. Automatic test equipment employing this Y-factor method require some means for separately controlling and measuring the temperature of the two resistors or generating suitable noise levels.
What is needed is a method of measuring noise figure F.